In general, this is slang for people who find tools on the Internet and use those tools to attack computer systems.
Specifically, a script kiddie is a person who seeks out a technology weakness over the Internet, in order to gain access to a computer system, without really understanding what he or she is exploiting, because the weakness was discovered by someone else. In other words, script kiddies are not very technologically sophisticated and they do not randomly look to target specific information or a specific company, but rather use knowledge of a known vulnerability to scan the entire Internet for a victim that possesses that vulnerability.
You may be amazed at how many people actually do this kind of thing, apparently because they can.
NetLingo Classification: Online Jargon